Boris Johnson has weighed in on the British government’s attempts to calm a potential diplomatic row sparked by its article 50 letter, assuring European capitals it had not intended to threaten EU security cooperation.

The foreign secretary tweeted ahead of a Nato meeting in Brussels that he would “stress that the UK’s commitment to the defence and security of Europe is unconditional”. Johnson’s intervention followed a frantic round of calls by British officials to EU diplomats in London, offering reassurances that Theresa May’s aim with the controversial article 50 letter had been merely to spell out the damaging consequences for both sides in failing to reach a deal.

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The wording of the letter – which was delivered to the president of the European council, Donald Tusk, on Wednesday – was widely interpreted to mean that security work could be undermined by a disadvantageous deal for the UK.

The Brexit secretary, David Davis, spent most of Wednesday afternoon on the phone to key European capitals, seeking to reassure diplomats that it would be wrong to interpret the letter as a threat.

Any attempt to play Britain’s security card so early in the negotiations was likely to set the talks off to the worst possible start.

Speaking in Malta on Friday, Tusk said he believed the row must have been due to a misunderstanding, given the common good in maintaining strong security ties.

“Especially after the terrorist attack in London, it must be clear that terrorism is our common problem,” he said. “That is why I rule out this kind of interpretation and speculation that security cooperation is used as a bargaining chip. It must be a misunderstanding … I am absolutely sure no one is interested in using security cooperation as a bargaining chip.”

Although many European diplomats had been angered by a previous threat – delivered in the prime minister’s Lancaster House speech in January – to turn the UK into an offshore deregulated competitor to the EU if the UK was not given a deal, some appeared to be willing to give her the benefit of the doubt this time.

One said: “Overall, the tone was much more positive and constructive. I think the passage about security was a statement of fact, not a threat. There was no linking security to securing a free trade deal.”

But Whitehall sources said senior figures in Britain’s intelligence services were “absolutely livid” at the way the letter was communicated to the press, and resented the suggestion that security could be traded off against the economy.

Theresa May’s article 50 letter was seen by some EU diplomats as a threat to end security cooperation. Photograph: Alastair Grant/AP

Key politicians in Brussels were more cynical about May’s motives. Elmar Brok, a key ally of Angela Merkel and senior member of her Christian Democratic Union party, claimed the letter was an attempt to scare eastern European states into championing Britain’s cause during Brexit negotiations.

But he said any such effort would be unsuccessful. “I do not see the point of threats,” said Brok, one of the longest-serving MEPs. “Britain relies on common security at least as much as we do. It will not have an impact on our behaviour in the negotiations.”

He added: “I think perhaps they want to make our eastern European partners nervous. It will mean the opposite of us splitting apart … that we increase the development of European development policy, as we have done in the last month or so. Britain is invited to take part a little bit or keep out. It is up to Britain.”

Guy Verhofstadt, the European parliament’s Brexit coordinator, also spoke out again on the issue. “A big mistake that we could make from both sides is to start with launching threats to each other,” he said.

“I find the letter of Mrs May very constructive, generally, but there is also one threat in it, in saying: ‘Look, we want also to cooperate with you on security issues in our common fight against terrorism but you have to give us a good deal on trade and economy.’

“It doesn’t work like that. You cannot use, or abuse, I should say, the security of citizens to have a good deal on something else.”

The former Bulgarian prime minister Sergei Stanishev said he had taken May’s letter as a threat, and warned that the tactic had no place at the negotiating table.

Stanishev, who was prime minister between 2005 and 2009, but is now president of the party of European Socialists in the European parliament, said: “I am concerned about the tone of Theresa May’s notification letter. She seems to suggest that she wants security cooperation to be a bargaining chip. Nobody should endanger British or European lives just to try and get the upper hand in a political process.

“Europe’s governments will not be blackmailed into making special concessions on economic issues by such thinly veiled threats.

“All of Europe, including the UK, is safer because of the close cooperation between us on security and defence issues. This ongoing cooperation is vital for the safety of our citizens and none of us want Brexit to threaten it.

“In the light of recent events around the world, it is indisputable that we are stronger together – and this applies to Britain as much as to the rest of the European Union.”

The British government insists May’s letter was intended as a constructive and warm statement of respect for the European Union, but the effort went awry as soon as parts of the British media read passages highlighting the consequences of no deal.

It made 11 references to security, and said that without a good deal “our cooperation in the fight against crime and terrorism would be weakened”.

Seeking to calm the row, Davis told the BBC: “We want a deal, and she was making the point that it’s bad for both of us if we don’t have a deal. Now that, I think, is a perfectly reasonable point to make and not in any sense a threat.”

The UK home secretary, Amber Rudd, whose responsibilities include intelligence and security, also denied there was a threat, but told Sky News: “If we left Europol [the EU’s law enforcement agency], then we would take our information ... with us.” It is understood she had been dispatched to counter the media narrative that the UK was threatening the EU, but she instead gave it further fuel.

May said on Thursday that Britain would probably have to leave Europol after Brexit but wanted to “maintain the degree of cooperation on these matters that we have currently”.

EU diplomats believe the UK will need to cooperate over terrorism and intelligence, and a threat to refuse to do so was simply not credible. Ursula von der Leyen, Germany’s defence minister, told Newsnight: “I do not expect that we’re going to bargain with security topics.”

The French also said they expected bilateral military cooperation to continue.

The British EU commissioner on security, Julian King, stressed on Thursday the progress the EU was making on data sharing and fighting terrorism.